A fun fact recently came up in a discussion about particle physics: the fact that elementary particles can have mass but take up no space. This seems a little weird at first. Based on our everyday experience, volume and mass seem to come hand in hand. But like so many other classical ideas, this preconception breaks down in the subatomic world.
How does that work? Well, volume and mass are actually very different concepts. Mass determines how a particle reacts to an external force, according to $F=ma$ (it also has to do with gravity based on its gravitational mass, but that's a whole separate story - one of these days I'll figure out what's up with general relativity, and in any case, subatomic particles don't interact with gravity enough to worry about), and in the world of elementary particles, a particle's mass is determined by its interaction with the Higgs field.
Volume, on the other hand, gives some measure of how much physical space an object occupies. In a particle like a proton, which has three quarks bound together in a complicated way by the strong nuclear force, that volume is determined by the quarks' interactions. It isn't the quarks that take up space, as much as the fact that they can't all occupy the same space, by the laws of quantum mechanics and inter-particle interactions. Similarly, the "space" that an atom takes up is dictated not by the space taken by protons and electrons, but by their electromagnetic attraction and the necessary space for electron orbitals and clouds. In a sense, we define the volume of an object in terms of its internal interactions. But if you take a look at a single particle like an electron, there aren't (as far as we know) any constituent parts. So what would it mean for there to be internal interactions to give it volume? It's practically nonsensical.
This is a really strange concept in the already-slightly-weird world of particle physics, but like so many such issues, it's a lot of fun to wrestle with.
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